SOLUTION: The manager of a peach orchard is trying to decide when to arrange for picking the peaches. If they are picked now, the average yield per tree will be 100 pounds, which can be sold

Question 583740: The manager of a peach orchard is trying to decide when to arrange for picking the peaches. If they are picked now, the average yield per tree will be 100 pounds, which can be sold for $.40 per pound. However, past experience shows that if the manager postpones the harvest a bit, the yield per tree will increase by about 5 pounds per week but the price will decrease about $.02 per pound per week.
a) Construct a function which gives the revenue per peach tree. Be sure to state what your variables represent.
Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
The manager of a peach orchard is trying to decide when to arrange for picking the peaches.
If they are picked now, the average yield per tree will be 100 pounds, which can be sold for $.40 per pound.
However, past experience shows that if the manager postpones the harvest a bit, the yield per tree will increase by about 5 pounds per week but the price will decrease about $.02 per pound per week.
:
a) Construct a function which gives the revenue per peach tree. Be sure to state what your variables represent.
:
Let w = no. of weeks passed 1st picking time
f(w) = revenue per tree
:
Rev = yield times price
f(w) = (100+5w)(.40-.02w)
FOIL
f(w) = 40 - 2w + 2w - .1w^2
Combine like terms. Arrange as a quadratic function
f(w) = -.1w^2 + 40

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